A064873 First of four sequences representing the lexicographical minimal decomposition of n in 4 squares: n = a(n)^2 + A064874(n)^2 + A064875(n)^2 + A064876(n)^2.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset

0,113

Comments

For n<112: a(n)=A072401(n), but A072401(112) = 1<>a(112)=2, as also A072401(112 - 1) = 1.

a(n) is the minimum k such that A072401(n - k^2) = 0. - Zhuorui He, Oct 23 2025

Links

Zhuorui He, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Square Numbers.

Index entries for sequences related to sums of squares.

Formula

A072401(n) = A057427(a(n)).

Conjecture: a(n) = A064874(n - A064874(n)^2). - Zhuorui He, Oct 23 2025

Example

a(25) = 0: 25 = a(25)^2 + A064874(25)^2 + A064875(25)^2 + A064876(25)^2 = 0 + 0 + 0 + 25 and the other decompositions (0, 0, 3, 4) and (1, 2, 2, 4) are greater than (0, 0, 0, 5).

Prog

(PARI) \\ Using Amiram Eldar's definition for A072401
A064873(n) = {my(k = 0); while(A072401(n - k^2), k += 1); k} \\ Zhuorui He, Oct 23 2025

Crossrefs

Cf. A064874, A064875, A064876, A071374, A072401.

Sequence in context: A323510 A044938 A072401 * A295659 A188436 A037823

Adjacent sequences: A064870 A064871 A064872 * A064874 A064875 A064876

Keyword

nonn

Author

Reinhard Zumkeller, Oct 10 2001

Status

approved